1) To have one's entire face covered in feces.
2) To become so intoxicated/high that you act like an asshole/whore/your math teacher and perform things/sexual acts that you would never do in your right mind.

1) Because my face is covered in shit, I am shit faced.
2) God, after those 15 bottle of scotch, I was shit faced and woke up next to my math teacher.